Method for designing three-dimensional trajectory of unmanned aerial vehicle based on wireless power transfer network

ABSTRACT

The invention discloses a method for designing a three-dimensional trajectory of an unmanned aerial vehicle based on a wireless power transfer network. The method comprises the following steps: establishing a downlink channel model of the wireless power transfer network; establishing a mathematical model based on maximizing energy harvested by a user, comprising three-dimensional position deployment of an unmanned aerial vehicle, allocation of a charging time, and generation of an energy beam pattern; jointly optimizing on design and analysis of low-complexity iterative algorithms for three-dimensional position deployment of the unmanned aerial vehicle, the charging time and an energy beam; and using branch and bound method to design a three-dimensional flight trajectory of the unmanned aerial vehicle.

TECHNICAL FIELD

The present invention relates to the field of wireless communicationtechnologies, and more particularly, to a method for designing athree-dimensional trajectory of an unmanned aerial vehicle based on awireless power transfer network.

BACKGROUND

Internet of Things (IoT), which enables heterogeneous smart devices tobe connected with each other and enables the devices to collect andexchange information, is used in smart home, smart transfer systems andsmart cities. According to Gartner, up to 840 million IoT devices wereused all over the world in 2017, and the number is expected to reach2.04 billion in 2020. Therefore, communication networks of nextgeneration need to support large-scale device communication services,while the traditional communication networks cannot support such a highdata requirement. The fifth generation network (5G) can make up fordefects of the current communication networks, and provides a gigabitdata rate and a low-delay communication service for connected devices.

In fact, the 5G network connects large-scale IoT devices and providesthe gigabit data rate and the low-delay communication, which consumes alot of power and shortens a service life of the IoT device, especially abattery-powered mobile device. A wireless power transfer (WPT) andenergy harvesting (EH) technology is one of promising technologies toprolong a service life of a node of the mobile device in the 5G network.The WPT technology is defined as to wirelessly transmit energy to anelectronic device through an energy source. Especially, inductivecoupling and magnetic resonance coupling are two energy transfertechnologies of the WPT. However transmission distances of the two areseveral centimeters and several meters respectively, which are notsuitable for long-distance energy transfer. On the other hand, energy iscontained in an electromagnetic wave (3 KHz to 300 GHz) and istransmitted to the electronic device by a radio frequency (RF) energytransfer technology, which has a transmission distance of tens ofkilometers. Therefore, the WPT technology based on the RF can be appliedto long-distance transmission. However, when a transmitting end and areceiving end are arranged in a disaster area or a remote mountainousarea, the two ends are far apart from each other, which leads toinefficient energy transmission.

Due to the advantages of self-organization, flexibility and mobility, anunmanned aerial vehicle can be deployed quickly in the remotemountainous area and a geographically restricted area, and replace alocal base station to provide reliable, economical and efficientwireless connection. Generally, the unmanned aerial vehicle comprises alow altitude platform (LAP) and a high altitude platform (HAP). The LAPhas a maximum altitude of 400 feet, while the HAP can be as high as 17km. On the other hand, the unmanned aerial vehicle may comprise a fixedwing and a rotor wing. In particular, a fixed-wing unmanned aerialvehicle can fly at a high speed for a long time, but cannot hover. Aquadrotor unmanned aerial vehicle can hover, but has a low flight speedand a short flight time.

Due to the multiple advantages of the unmanned aerial vehicle, atechnology of integrating the unmanned aerial vehicle with the wirelesspower transfer technology has been proposed in recent years and appliedin many occasions to charge a low-power mobile device. However, limitedby a capacity of a battery on a board, the flight time of the unmannedaerial vehicle is limited. Therefore, how to reduce aerodynamicconsumption and maximize an energy efficiency of the unmanned aerialvehicle to extend a time of endurance of the unmanned aerial vehicle isresearched by existing scholars. In addition, energy harvesting isimproved and the flight time of the unmanned aerial vehicle is prolongedby optimizing a flight trajectory, position deployment, charging timeallocation of the unmanned aerial vehicle, etc.

SUMMARY

Aiming at the defects in the prior art, the present invention isintended to establish a downlink channel model of a wireless powertransfer network and a mathematical model based on maximizing energyharvested by a user, and propose a low-complexity iterative algorithmfor jointly optimizing a three-dimensional position deployment of anunmanned aerial vehicle, a charging time and an energy beam, so as tomaximize the energy harvested by the user while meeting a user coveragerequirement in an area. In addition, the present invention establishes amathematical model for minimizing a flight trajectory, and designs aminimum flight distance by using Branch and Bound, so as to prolong atime of endurance of the unmanned aerial vehicle while minimizing theflight distance. The technical problems to be solved by the presentinvention are as follows:

problem 1: the downlink channel model of the wireless power transfer(WPT) network is established in combination with a three-dimensionaldynamic energy beam forming technology and a direct path;

problem 2: the mathematical model based on maximizing the energyharvested by the user is established for the downlink channel model;

problem 3: the low-complexity iterative algorithm for jointly optimizingthe three-dimensional position deployment of the unmanned aerialvehicle, the charging time and the energy beam is analyzed and designedaccording to the specific mathematical model; and

problem 4: the three-dimensional flight trajectory of the unmannedaerial vehicle is designed by using the Branch and Bound according to athree-dimensional hovering position of the unmanned aerial vehicle.

The objective of the present invention is achieved at least by one ofthe following technical solutions.

A method for designing a three-dimensional trajectory of an unmannedaerial vehicle based on a wireless power transfer network comprises thefollowing steps:

step 1: establishing a downlink channel model of the wireless powertransfer network: combining three-dimensional dynamic energy beamforming with a direct path to form a channel model between an unmannedaerial vehicle and a user;

step 2: establishing a mathematical model based on maximizing energyharvested by a user, comprising mathematical expressions for determiningan optimization variable, an objective function and a constraintcondition;

step 3: establishing a low-complexity iterative algorithm for jointlyoptimizing three-dimensional position deployment of the unmanned aerialvehicle, a charging time and an energy beam; and

step 4: designing a three-dimensional flight trajectory of the unmannedaerial vehicle based on Branch and Bound.

Further, in the step 1:

the wireless power transfer network comprises a quadrotor unmannedaerial vehicle and K users randomly distributed on land, the unmannedaerial vehicle is provided with a linear array comprising M antennaelements, while the users on land are provided with a single antenna; aland geometric area is divided into Γ service areas; a positioncoordinate of a user k is z_(k)=(x_(k), y_(k), 0), and k∈{1, . . . , K}is an index of an user set; a three-dimensional position of the unmannedaerial vehicle is z_(u)=(x_(u), y_(u), h), and h represents an altitudeof the unmanned aerial vehicle; and a wireless channel between theunmanned aerial vehicle and the user k is dominated by the direct path,so that a channel vector h_(k) is as follows:

h _(k)=√{square root over (β₀ d _(k) ^(α))}α(θ,ϕ),  (1)

wherein n_(k)=β₀d_(k) ⁻¹ is a multiplexing coefficient, and β₀ is achannel power gain when a reference distance is 1 m; in addition,d_(k)=√{square root over ((x_(k)−x_(u))²+(y_(k)−y_(u))₂+h²)} is adistance between the unmanned aerial vehicle and the user k, α is a pathloss coefficient; and a(θ, ϕ)) is a direction vector, which is expressedas follows:

a(θ,ϕ)=[1,e ^(j2π/λd) ^(array) ^(sin θ cos ϕ) , . . . ,e ^(j(M-1)2π/λd)^(array) ^(sin θ cos ϕ)]^(T),  (2)

wherein λ and d_(array) are respectively a wavelength and an elementspacing in the linear array, and an elevation angle θ and an azimuthangle ϕ are known quantities; therefore, a channel gain between theunmanned aerial vehicle and the user k is expressed as follows:

$\begin{matrix}{{\left| {h_{k}^{H}w} \right|^{2} = {\frac{\beta_{0}}{\left\lbrack {\left( {x_{k} - x_{u}} \right)^{2} + \left( {y_{k} - y_{u}} \right)^{2} + h^{2}} \right\rbrack^{\alpha/2}}{{{\alpha^{H}\left( {\theta,\phi} \right)}w}}^{2}}},} & (3)\end{matrix}$

wherein H represents conjugate transpose, w is a beam weight vector, anda main lobe direction is controlled by adjusting a weight value; andE(θ, ϕ))=a^(H)(θ, ϕ)w is a synthesized pattern of the linear array;

the linear array installed on the unmanned aerial vehicle as atransmitting end is divided into t sub-arrays, and each sub-arrayindependently generates an energy beam to aim at a certain user;therefore, for the linear array comprising M antenna elements, an arrayfactor and a synthesized pattern are expressed as follows:

$\begin{matrix}{{{AF} = {\sum\limits_{m = 1}^{M = 1}{I_{m} \times e^{{j{({m - 1})}}{({{\kappa\beta\sin\theta\cos\phi} + \beta})}}}}},} & (4) \\{{{E\left( {\theta,\phi} \right)} = {\sum\limits_{m = 1}^{M = 1}{{p_{m}\left( {\theta,\phi} \right)}I_{m} \times e^{{j{({m - 1})}}{({{\kappa d{sin\theta cos\phi}} + \beta})}}}}},} & (5)\end{matrix}$

wherein κ=2π/λ, p_(m)(θ, ϕ)) and I_(m) are respectively an elementpattern and an excitation amplitude of an m^(th) antenna element, and βis a uniformly graded phase; and d is an array element spacing, and e isa natural constant.

Further, in the step 2, total energy used by the user k is expressed asfollows:

$\begin{matrix}{Q_{k} = \left. \xi_{k} \middle| {h_{k}^{H}w} \middle| {}_{2}{P_{0}\tau_{k,\gamma}} \right.} & {(6)} \\{{= \frac{\left. {\xi_{k}\beta_{0}P_{0}\tau_{k,\gamma}} \middle| {E\left( {\theta,\phi} \right)} \right|^{2}}{\left\lbrack {\left( {x_{k} - x_{u}} \right)^{2} + \left( {y_{k} - y_{u}} \right)^{2} + h^{2}} \right\rbrack^{\alpha/2}}},} & {{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~}(7)}\end{matrix}$

wherein ξ_(k) is an energy conversion efficiency, 0<ξ_(k)<1, P₀ is atransmitting power of the unmanned aerial vehicle, and τ_(k,γ) is acharging time of the user k in a γ^(th) area;

Therefore, optimization variables of the mathematical model based onmaximizing the energy harvested by the user comprise:

-   -   1) a two-dimensional coordinate of the unmanned aerial vehicle,        which is namely z_(u)=(x_(u), y_(u), 0);    -   2) an altitude h of the unmanned aerial vehicle;    -   3) an energy beam pattern E(θ, ϕ) of the linear array; and    -   4) a charging time τ_(k,γ) of the user k located in the γ^(th)        service area;

constraint conditions of the mathematical model based on maximizing theenergy harvested by the user comprise:

(1) a maximum horizontal distance between the unmanned aerial vehicleand the user being no more than a coverage radius of the unmanned aerialvehicle: ∥z_(k)−z_(u)∥²≤h² tan² Θ; and Θ being a beam width;

(2) a total charging time of the unmanned aerial vehicle in all the Γservice areas being no more than a charging period T: Σ_(γ=1) ^(Γ)τ_(k,γ)=T;

(3) the altitude of the unmanned aerial vehicle being constrained to:h_(min)<h<h_(max), wherein h_(min) and h_(max) are respectively a lowestaltitude and a highest altitude that the unmanned aerial vehicle is ableto reach;

the mathematical model based on maximizing the energy harvested by theuser is as follows:

$\begin{matrix}{\max\limits_{z_{u},h,\tau_{k,\gamma},{E{({\theta,\phi})}}}{\sum\limits_{k = 1}^{K}\frac{\xi_{k}\beta_{0}P_{0}\tau_{k,\gamma}{{E\left( {\theta,\phi} \right)}}^{2}}{\left\lbrack {{{z_{k} - z_{u}}}^{2} + h^{2}} \right\rbrack^{\alpha/2}}}} & \left( {8a} \right) \\{{{s.t.{{z_{k} - z_{u}}}^{2}} \leq {h^{2}\tan^{2}\Theta}},} & \left( {8b} \right) \\{{{\sum\limits_{\gamma = 1}^{\Gamma}\tau_{k,\gamma}} = T},} & \left( {8c} \right) \\{h_{\min} < h < {h_{\max}.}} & \left( {8d} \right)\end{matrix}$

Further, in the step 3, system parameters, a value range of theoptimization variables and the constraint conditions of the wirelesspower transfer network are set; and the low-complexity algorithmcomprises the following steps:

S1. fixing the altitude h, the beam pattern E(θ, ϕ) and the chargingtime τ_(k,γ) of the unmanned aerial vehicle, and solving the objectivefunction with respect to a two-dimensional coordinate (x_(u), y_(u)) ofthe unmanned aerial vehicle by using sequential unconstrained convexminimization (SUCM) at the moment;

S2. fixing the beam pattern E(θ, ϕ) and the charging time τ_(k,γ) basedon the two-dimensional coordinate (x_(u), y_(u)) of the unmanned aerialvehicle, the objective function becoming a monotone decreasing functionwith respect to the altitude h at the moment, and obtaining an optimalaltitude

${h^{*} = {\max\left\{ {\frac{\sqrt{D_{\max}}}{\tan\Theta},h_{\min}} \right\}}},$

while D_(max)=max_(k=1, . . . , K) D_(k), and D_(k)=∥z_(k)−z_(u)∥²;

S3. fixing the charging time τ_(k,γ) based on the three-dimensionalposition deployment of the unmanned aerial vehicle, and optimizing theenergy beam pattern by using a multiobjective evolutionary algorithmbased on decomposition (MOEA/D), wherein the energy beam patterncomprises an antenna gain, a minor lobe voltage level and a beam width,and since the antenna gain, the minor lobe voltage level and the beamwidth are functions with respect to a phase β, the antenna gain, theminor lobe voltage level and the beam width optimized are expressed as amultiobjective optimization problem with respect to the phase β; and

S4. based on the optimal three-dimensional position, the optimalaltitude and the optimal energy beam pattern of the unmanned aerialvehicle which are solved, solving the objective function which is alinear programming problem of a function with respect to the chargingtime τ_(k,γ) at the moment by using a standard convex optimization tool.

Further, the step S1 comprises the following steps.

$S^{(1)} = \left\{ {t \in {{{R_{-}^{K}: -}\Sigma_{k = 1}^{K}t_{k}} \leq \frac{1}{Ϛ}}} \right\}$

S1.1. initializing iteration times m, a polyhedron

${v^{(1)} = {\left\{ {{{- \frac{1}{Ϛ}}e_{k}} \in {{R^{K}:1} \leq k \leq K}} \right\}\bigcup\left\{ 0 \right\}}},$

and a vertex set wherein R⁻ ^(K) is a K-dimensional negative realnumber, and R^(K) is a K-dimensional non-negative real number; a bestfeasible solution of max_(t∈{tilde over (D)})v^(T)t is t*, satisfyingq(t₀)<q(t*), wherein t₀ is a known quantity, while t* is a solvedquantity; q(t)=A_(k)t^(−α/2), and A_(k)=ξ_(k)β₀P₀τ_(k,γ)|E(θ, ϕ)|²;

>0; {tilde over (D)}={t−t₀|t∈D}, D={t∈R₊ ^(K):ε_(k)(x_(u), y_(u))≤t_(k),=1, . . . , K}, and D is a domain of definition of t, {tilde over (D)}is a domain of definition of t−t₀, and ε_(k)(x_(u),y_(u))=(x_(k)−x_(u))²+(y_(k)−y_(u))²+h²;

S1.2. for all −w=v, v∈v^(m), solving min_(x) _(u) _(,y) _(u) Σ_(k=1)^(K) w_(k)[(x_(k)−x_(u))²+(y_(k)−y_(u))²+h²]^(α/2) to obtain optimalvalues μ(w) and (x_(u)*, y_(u)*), wherein

${x_{u}^{*} = \frac{\Sigma_{k = 1}^{K}w_{k}x_{k}}{\Sigma_{k = 1}^{K}w_{k}}},{{{and}\mspace{14mu} y_{u}^{*}} = \frac{\Sigma_{k = 1}^{K}w_{k}y_{k}}{\Sigma_{k = 1}^{K}w_{k}}},$

wherein w=[w₁, . . . , w_(k)] is a k-dimensional vector, and v^(m) is am-dimensional vector;

S1.3. judging whether an inequality max_(−w∈v) _(m) −μ(w)+w^(T)t₀≤1 istrue, and if the inequality is true, returning to the S1.1; and if theinequality is not true, skipping to the step S1.4;

S1.4. obtaining {tilde over (w)}=[{tilde over (w)}₁, . . . , {tilde over(w)}_(k)] through max_(−w∈v) _(m) −μ(w)+w^(T)t₀, and {tilde over(t)}_(k)=ε_(k)({tilde over (x)}_(u), {tilde over (y)}_(u)), k=1, . . . ,K, wherein ∈_(k)({tilde over (x)}_(u), {tilde over(y)}_(u))=(x_(k)−{tilde over (x)}_(u))²+(y_(k)−{tilde over(y)}_(u))²+h²; and after obtaining {tilde over (w)} and {tilde over(t)}_(k), further obtaining a two-dimensional position ({tilde over(x)}_(u), {tilde over (y)}_(u)) of the unmanned aerial vehicle, while({tilde over (x)}_(u), {tilde over (y)}_(u)) is obtained respectively bythe following formulas

${{\overset{˜}{x}}_{u} = {{\frac{\Sigma_{k = 1}^{K}{\overset{\sim}{w}}_{k}x_{k}}{\Sigma_{k = 1}^{K}{\overset{\sim}{w}}_{k}}\mspace{14mu}{and}\mspace{14mu}{\overset{˜}{y}}_{u}} = \frac{\Sigma_{k = 1}^{K}{\overset{\sim}{w}}_{k}y_{k}}{\Sigma_{k = 1}^{K}{\overset{\sim}{w}}_{k}}}},$

S1.5. judging whether an inequality q({tilde over (t)})≤q(t*) is true,and if the inequality is true, updating t*={tilde over (t)}, wherein{tilde over (t)}=[{tilde over (t)}₁, . . . , {tilde over (t)}_(k)];otherwise, calculating ϑ and S^((m+1)) by using ϑ=sup{ρ:q(t₀+ρ*({tildeover (t)}−t₀))≤q(t*)} and

$S^{({m + 1})} = {S^{(m)}\bigcap\left\{ {{t^{T}\left( {\overset{\sim}{t} - t_{0}} \right)} \leq \frac{1}{\vartheta}} \right\}}$

respectively, wherein ε≥1; and under a condition of obtaining variablesρ and ϑ, using an analytic center cutting-plane method (ACCPM) algorithmto cut the polyhedron; and

S1.6. judging whether iteration times m of the algorithm satisfy settimes, if the set times are not satisfied, m:

m+1, returning to the step S1.2, and if the set times are satisfied,obtaining the two-dimensional position (x_(u)*, y_(u)*) of the unmannedaerial vehicle.

Further, in the step S2, the beam pattern E(θ, ϕ) and the charging timeτ_(k,γ) are fixed based on the obtained two-dimensional position of theunmanned aerial vehicle, and the optimization problem is expressed asfollows at the moment:

$\begin{matrix}{\max\limits_{h}{\sum\limits_{k = 1}^{K}\frac{A_{k}}{\left\lbrack {D_{k} + h^{2}} \right\rbrack^{\alpha/2}}}} & \left( {9a} \right) \\{{{s.t.\mspace{14mu} D_{\max}} \leq {h^{2}{\tan\Theta}}},} & \left( {9b} \right) \\{{h_{\min} \leq h \leq h_{\max}},} & \left( {9c} \right)\end{matrix}$

wherein a constraint condition D_(max)≤h² tan Θ shows that a distancebetween the unmanned aerial vehicle and all the users is not allowed toexceed the coverage radius of the unmanned aerial vehicle; and since theoptimization problem is a convex optimization problem, while theobjective function is a monotone decreasing function with respect to thealtitude h of the unmanned aerial vehicle, then the optimal altitude isas follows:

$\begin{matrix}{h^{*} = {\max\left\{ {\frac{\sqrt{D_{\max}}}{\tan\Theta},h_{\min}} \right\}}} & (10)\end{matrix}$

Further, the step S3 comprises the following steps:

S3.1. fixing the charging time τ_(k,γ) based on the obtainedthree-dimensional position (x_(u)*, y_(u)*, h*) of the unmanned aerialvehicle, so that the objective function is expressed as follows:

$\begin{matrix}{{{\max{\sum\limits_{k = 1}^{K}{\eta_{k}{{E\left( {\theta,\ \phi} \right)}}^{2}}}},{where}}\;{\eta_{k} = \frac{\xi_{k}\beta_{0}P_{0}\tau_{k,\gamma}}{\left\lbrack {{{z_{k} - z_{u}}}^{2} + h^{2}} \right\rbrack^{\alpha/2}}}} & (11)\end{matrix}$

is a constant; therefore, the objective function is expressed asfollows:

$\begin{matrix}{\max{\sum\limits_{k = 1}^{K}{{E\left( {\theta,\phi} \right)}}^{2}}} & (12)\end{matrix}$

S3.2. modeling into a multiobjective optimization problem, and theobjective functions of the multiobjective optimization problem areexpressed as follows:

min F(β)=(ƒ₁(β),ƒ₂(β),ƒ₃(β))^(T),  (13a)

s.t.β∈R ^(M),  (13b)

wherein ƒ₁(β)=SLL(β): an objective function of a minimized minor lobevoltage level with respect to β;

${f_{2}(\beta)} = {\frac{1}{{E\left( {\theta,\phi} \right)}}\text{:}}$

an objective function of a maximized antenna gain with respect to β; and

${{f_{3}(\beta)} = \frac{1}{\Theta }}\text{:}$

an objective function of a maximized beam width θ of the array antennawith respect to β;

S3.3. definition of domination: assuming that u, v∈R^(m), u dominatingv, and if and only if

u _(i) ≤v _(i) ,∀i∈{1, . . . ,m},  (14)

u _(j) <v _(j) ,∀i∈{1, . . . ,m},  (15)

S3.4. definition of Pareto optimality: x*∈Ω being the Pareto optimality,satisfying a condition that no other solution x∈Ω exists, so that F(x)dominates F(x*), and F(x*) being a Pareto optimal vector; and

S3.5. aiming at the constructed multiobjective optimization problem,using the MOEA/D to generate a directional beam.

Further, the MOEA/D has the specific steps as follows:

A1. inputting: the constructed multiobjective optimization problem;Iter: iteration times; N_(pop)a number of subproblems; K¹, . . . , K^(N)^(pop) : a weight vector; and T_(nei): a number of neighbor vectors ofeach weight vector;

A2. initializing: a set EP=Ø;

A3. for each i=1, . . . , N_(pop), setting ℏ(i)={i₁, . . . , i_(T)_(net) } as an index of the neighbor vector according to T_(nei) weightvectors K¹, . . . , K^(N) ^(pop) near an Euclidean distance weight i themost;

A4. randomly generating an original group β=[β₁, . . . , β_(N) _(pop) ];and setting FV_(i)=F(β_(i));

A5. for each j=1, . . . , d, initializing z=(z₁, . . . , z_(j), . . . ,z_(d))^(T) through z_(j)=min{ƒf_(j)(β), β∈R^(M)}, wherein d is a numberof objective functions;

A6. updating: for each i=1, . . . , N_(pop), randomly selecting twoindexes κ and ι from a set ℏ(i), and combining β_(κ) and β_(ι) togenerate a new feasible solution y by a differential evolutionalgorithm; for each j=1, . . . , d, if z_(j)>ƒ_(j)(y), settingz_(j)=ƒ_(j)(y); at the moment, z_(j) being a current optimal solution;for each j∈ℏ(i), if g^(te)(y|κ^(j), z)≤g^(te)(β_(j)|κ^(j), z), settingβ_(j)=y and FV_(j)=F(y), wherein g^(te)(y|κ^(j),z)=max_(1≤j≤d){κ^(j)|ƒ_(j)(y)−z_(j)}; eliminating a solution dominatedby F(y) from the set EP; and if no vector exists in the set EP todominate F(y), adding F(y) into the set EP;

A7. stopping criterion: if the iteration times satisfy Iter, enteringinto step A8; otherwise, returning to the updating step A6; and

A8. outputting: constantly updating a non-dominant solution EP duringsearching, and finally obtaining an optimal domination set EP*, and aPareto optimal solution β*, so that EP*∈β*.

Further, in the step S4, based on the obtained three-dimensionalposition (x_(u)*, y_(u)*, h*) of the unmanned aerial vehicle and thebeam pattern E*(θ, ϕ), the original problems become:

$\begin{matrix}{\max\limits_{\tau_{k,\gamma}}{\sum\limits_{k = 1}^{K}\frac{\xi_{k}\beta_{0}P_{0}\tau_{k,\gamma}{{E\left( {\theta,\phi} \right)}}^{2}}{\left\lbrack {{{z_{k} - z_{u}}}^{2} + h^{2}} \right\rbrack^{\alpha/2}}}} & \left( {16a} \right) \\{{{s.t.{\sum\limits_{\gamma = 1}^{\Gamma}\tau_{k,\gamma}}} = T};} & \left( {16b} \right)\end{matrix}$

The solution of the above problems may lead to serious fairnessproblems, and the reason is that when the total energy harvested in acertain area is significantly greater than that in other areas, thecharging time in this area is longer; and in order to solve thisdifficulty, the following new optimization problems are proposed:

$\begin{matrix}{\max\limits_{\tau_{k,\gamma}}{\sum\limits_{k = 1}^{K}{\min\limits_{k \in K}\frac{\xi_{k}\beta_{0}P_{0}\tau_{k,\gamma}{{E\left( {\theta,\ \phi} \right)}}^{2}}{\left\lbrack {\left( {x_{k} - x_{u,\gamma}} \right)^{2} + \left( {\gamma_{k} - \gamma_{u,\gamma}} \right)^{2} + h_{\gamma}^{2}} \right\rbrack^{\alpha/2}}}}} & \left( {17a} \right) \\{{{s.t.{\sum\limits_{\gamma = 1}^{\Gamma}\tau_{k,\gamma}}} = T};} & \left( {17b} \right)\end{matrix}$

at the moment, the three-dimensional position of the unmanned aerialvehicle in the area γ is (x_(u,y), y_(u,y), h_(y)); and in order tosolve this problem, an auxiliary variable t is introduced, then:

$\begin{matrix}{\mspace{79mu}{\max\limits_{\tau_{k,\gamma}}t}} & \left( {18a} \right) \\{\mspace{79mu}{{{s.t.{\sum\limits_{\gamma = 1}^{\Gamma}{\tau_{k,\gamma}{\varrho\left( {x_{u,\gamma},\gamma_{u,\gamma},h_{\gamma}} \right)}}}} \geq t},}} & \left( {18b} \right) \\{\mspace{79mu}{{{{\sum\limits_{\gamma = 1}^{\Gamma}\tau_{k,\gamma}} = T},\mspace{79mu}{wherein}}\text{}{{{\varrho\left( {x_{u,\gamma},\gamma_{u,\gamma},h_{\gamma}} \right)} = {\sum_{k = 1}^{K}\frac{\xi_{k}\beta_{0}P_{0}\tau_{k,\gamma}{{E\left( {\theta,\phi} \right)}}^{2}}{\left\lbrack {\left( {x_{k} - x_{u,\gamma}} \right)^{2} + \left( {y_{k} - y_{u,\gamma}} \right)^{2} + h_{\gamma}^{2}} \right\rbrack^{\alpha/2}}}};}}} & \left( {18c} \right)\end{matrix}$

and the optimization problem is a linear programming problem, which maybe solved by a general convex optimization tool.

In the step 4, an objective function of optimization problems based on aminimized flight distance is the minimized flight distance, which isexpressed as follows:

$\begin{matrix}{{\underset{a \neq b}{\sum\limits_{a = 0}^{\Gamma}}{\underset{a \neq b}{\sum\limits_{b = 0}^{\Gamma}}{d_{ab}x_{ab}}}},} & (19)\end{matrix}$

optimization variables of the optimization problems are able to beexpressed as:

1> a distance d_(ab)=√{square root over((x_(a)−x_(b))²+(y_(a)−y_(b))²+(h_(a)−h_(b))²)} between a hoveringposition a with a coordinate (x_(a), y_(a), h_(a)) and a hoveringposition b with a coordinate (x_(b), y_(b), h_(b)); and

2> a non-negative integer x_(ab)∈{0,1};

constraint conditions of the optimization problem comprise:

1] a number of times of flying from the hovering position a to thehovering position b being no more than 1:

${{\sum_{\underset{a \neq b}{a = 0}\ }^{\Gamma}x_{ab}} = 1};$

2] a number of times of flying from the hovering position b to thehovering position a being no more than 1:

${{\sum_{\underset{b \neq a}{b = 0}\ }^{\Gamma}x_{ab}} = 1};$

3] a number of times of flying from the hovering position a to anoriginal position 0 is no more than 1: Σ_(a=1) ^(Γ) x_(a0)=1; and

4] a number of times of staying on the hovering position being no morethan γ: μ_(a)−μ_(b)+γx_(ab)≤γ−1, wherein γ>Γ, μ_(a) and μ_(b) arearbitrary real variables, and a=1, . . . , Γ, b=1, . . . , Γ;

the optimization problems based on the minimized flight distance are asfollows:

$\begin{matrix}{\min{\underset{a \neq b}{\sum\limits_{a = 0}^{\Gamma}}{\underset{b \neq a}{\sum\limits_{b = 0}^{\Gamma}}{d_{ab}x_{ab}}}}} & \left( {20a} \right) \\{{{s.t.{\underset{a \neq b}{\sum\limits_{a = 0}^{\Gamma}}x_{ab}}} = 1},} & \left( {20b} \right) \\{{{\underset{b \neq a}{\sum\limits_{b = 0}^{\Gamma}}x_{ab}} = 1},} & \left( {20c} \right) \\{{{\sum\limits_{a = 1}^{\Gamma}x_{a0}} = 1},} & \left( {20d} \right) \\{{{\mu_{a} - \mu_{b} + {\gamma x_{ab}}} \leq {\gamma - 1}};} & \left( {20e} \right)\end{matrix}$

the steps for obtaining the optimal flight trajectory by the Branch andBound are as follows:

firstly, decomposing all flight trajectory sets, namely feasiblesolutions, into smaller sets by the low-complexity algorithm, andcalculating a lower bound of each set; then, containing a set of asmallest lower bound in all the sets in the optimal trajectory; andfinally, forming all the selected sets into the optimal flighttrajectory.

Compared with the prior art, the present invention has the followingadvantages and beneficial effects.

According to the method for designing the three-dimensional flighttrajectory based on the wireless power transfer network of the unmannedaerial vehicle and allocating the charging time provided by the presentinvention, the downlink channel model of the wireless power transfernetwork and the mathematical model based on maximizing the energyharvested by the user are established, and the low-complexity algorithmfor jointly optimizing the three-dimensional position deployment of theunmanned aerial vehicle, the charging time and the energy beam isproposed, so as to maximize the energy harvested by the user whilemeeting a user coverage requirement in an area. In addition, the presentinvention establishes a mathematical model for minimizing a flighttrajectory, and designs a minimum flight distance by using the Branchand Bound, so as to prolong a time of endurance of the unmanned aerialvehicle while minimizing the flight distance. Compared with asingle-beam WPT system, a single-antenna WPT system and a WPT systembased on two-dimensional unmanned aerial vehicle deployment, theproposed three-dimensional dynamic multi-beam WPT system has a higherenergy harvesting efficiency.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flowchart of a method for designing a three-dimensionalflight trajectory based on a wireless power transfer network of anunmanned aerial vehicle and allocating a charging time in the embodimentof the present invention;

FIG. 2 is a diagram of a multi-beam wireless power transfer networkmodel of the unmanned aerial vehicle in the embodiment of the presentinvention;

FIG. 3 is a diagram of a receiving and transmitting structure based onwireless power transfer of the unmanned aerial vehicle in the embodimentof the present invention; and

FIG. 4 is a flowchart of a low-complexity iterative algorithm forjointly optimizing a three-dimensional position deployment of theunmanned aerial vehicle, a charging time and an energy beam in theembodiment of the present invention.

DETAILED DESCRIPTION

The specific implementation of the present invention is furtherdescribed in detail hereinafter with reference to the embodiments andthe accompanying drawings, but the implementation modes of the presentinvention are not limited to this.

As shown in FIG. 1, a method for designing a three-dimensionaltrajectory of an unmanned aerial vehicle based on a wireless powertransfer network comprises the following steps.

In step 1, a downlink channel model of the wireless power transfernetwork is established: as shown in FIG. 2 and FIG. 3, three-dimensionaldynamic energy beam forming is combined with a direct path to form achannel model between an unmanned aerial vehicle and a user.

The wireless power transfer network comprises a quadrotor unmannedaerial vehicle and K users randomly distributed on land, the unmannedaerial vehicle is provided with a linear array comprising M antennaelements, while the users on land are provided with a single antenna; aland geometric area is divided into r service areas; a positioncoordinate of a user k is z_(k)=(x_(k), y_(k), 0), and k∈{1, . . . , K}is an index of an user set; a three-dimensional position of the unmannedaerial vehicle is z_(u)=(x_(u), y_(u), h), and h represents an altitudeof the unmanned aerial vehicle; and a wireless channel between theunmanned aerial vehicle and the user k is dominated by the direct path,so that a channel vector h_(k) is as follows:

h _(k)=√{square root over (β₀ d _(k) ^(α))}α(θ,ϕ),  (1)

wherein n_(k)=β₀d_(k) ⁻¹ is a multiplexing coefficient, and β₀ is achannel power gain when a reference distance is 1 m; in addition,d_(k)=√{square root over ((x_(k)−x_(u))²+(y_(k)−y_(u))²+h²)} is adistance between the unmanned aerial vehicle and the user k, α is a pathloss coefficient; and a(θ, ϕ) is a direction vector, which is expressedas follows:

a(θ,ϕ)=[1,e ^(j2π/λd) ^(array) ^(sin θ cos ϕ) , . . . ,e ^(j(M-1)2π/λd)^(array) ^(sin θ cos ϕ)]^(T),  (2)

wherein λ and d_(array) are respectively a wavelength and an elementspacing in the linear array, and an elevation angle θ and an azimuthangle ϕ are known quantities; therefore, a channel gain between theunmanned aerial vehicle and the user k is expressed as follows:

$\begin{matrix}{{\left| {h_{k}^{H}w} \right|^{2} = {\frac{\beta_{0}}{\left\lbrack {\left( {x_{k} - x_{u}} \right)^{2} + \left( {y_{k} - y_{u}} \right)^{2} + h^{2}} \right\rbrack^{\alpha/2}}{{{a^{H}\left( {\theta,\ \phi} \right)}w}}^{2}}},} & (3)\end{matrix}$

wherein H represents conjugate transpose, w is a beam weight vector, anda main lobe direction is controlled by adjusting a weight value; andE(θ, ϕ)=a^(H)(θ, ϕ)w is a synthesized pattern of the linear array;

the linear array installed on the unmanned aerial vehicle as atransmitting end is divided into t sub-arrays, and each sub-arrayindependently generates an energy beam to aim at a certain user;therefore, for the linear array comprising M antenna elements, an arrayfactor and a synthesized pattern are expressed as follows:

$\begin{matrix}{{{AF} = {\sum\limits_{m = 1}^{M = 1}{I_{m} \times e^{{j{({m - 1})}}{({{\kappa\beta\sin\theta\cos\phi} + \beta})}}}}},} & (4) \\{{{E\left( {\theta,\ \phi} \right)} = {\sum\limits_{m = 1}^{M = 1}{{p_{m}\left( {\theta,\ \phi} \right)}I_{m} \times e^{{j{({m - 1})}}{({{\kappa\; d\;\sin\;{\theta cos\phi}} + \beta})}}}}},} & (5)\end{matrix}$

wherein κ=2π/λ, p_(m)(θ, ϕ) and I_(m) are respectively an elementpattern and an excitation amplitude of an m^(th) antenna element, and βis a uniformly graded phase; and d is an array element spacing, and e isa natural constant.

In step 2, a mathematical model based on maximizing energy harvested bya user is established, comprising mathematical expressions fordetermining an optimization variable, an objective function and aconstraint condition.

Total energy used by the user k is expressed as follows:

$\begin{matrix}{Q_{k} = {\xi_{k}{{h_{k}^{H}w}}^{2}P_{0}\tau_{k,\gamma}}} & (6) \\{{= \frac{\left. {\xi_{k}\beta_{0}P_{0}\tau_{k,\gamma}} \middle| {E\left( {\theta,\phi} \right)} \right|^{2}}{\left\lbrack {\left( {x_{k} - x_{u}} \right)^{2} + \left( {y_{k} - y_{u}} \right)^{2} + h^{2}} \right\rbrack^{\alpha/2}}},} & (7)\end{matrix}$

wherein ξ_(k) is an energy conversion efficiency, 0<ξ_(k)<1, P₀ is atransmitting power of the unmanned aerial vehicle, and τ_(k,γ) is acharging time of the user k in a γ^(th) area;

Therefore, optimization variables of the mathematical model based onmaximizing the energy harvested by the user comprise:

-   -   1) a two-dimensional coordinate of the unmanned aerial vehicle,        which is namely z_(u)=(x_(u), y_(u), 0);    -   2) an altitude h of the unmanned aerial vehicle;    -   3) an energy beam pattern E(θ, ϕ) of the linear array; and    -   4) a charging time τ_(k,γ) of the user k located in the γ^(th)        service area;

constraint conditions of the mathematical model based on maximizing theenergy harvested by the user comprise:

(1) a maximum horizontal distance between the unmanned aerial vehicleand the user being no more than a coverage radius of the unmanned aerialvehicle: ∥z_(k)−z_(u)∥²≤h² tan² Θ; and Θ being a beam width;

(2) a total charging time of the unmanned aerial vehicle in all the Γservice areas being no more than a charging period T: Σ_(γ=1) ^(Γ)τ_(k,γ)=T;

(3) the altitude of the unmanned aerial vehicle being constrained to:h_(min)<h<h_(max), wherein h_(min) and h_(max) are respectively a lowestaltitude and a highest altitude that the unmanned aerial vehicle is ableto reach;

the mathematical model based on maximizing the energy harvested by theuser is as follows:

$\begin{matrix}{\max\limits_{z_{u},h,\tau_{k,\gamma},{E{({\theta,\phi})}}}{\sum\limits_{k = 1}^{K}\frac{\xi_{k}\beta_{0}P_{0}\tau_{k,\gamma}{{E\left( {\theta,\phi} \right)}}^{2}}{\left\lbrack {{{z_{k} - z_{u}}}^{2} + h^{2}} \right\rbrack^{\alpha/2}}}} & \left( {8a} \right) \\{{{s.t.{{z_{k} - z_{u}}}^{2}} \leq {h^{2}\tan^{2}\Theta}},} & \left( {8b} \right) \\{{{\sum\limits_{\gamma = 1}^{\Gamma}\tau_{k,\gamma}} = T},} & \left( {8c} \right) \\{h_{\min} < h < {h_{\max}.}} & \left( {8d} \right)\end{matrix}$

In step 3, a low-complexity iterative algorithm for jointly optimizingthree-dimensional position deployment of the unmanned aerial vehicle, acharging time and an energy beam is established.

As shown in FIG. 4, system parameters, a value range of the optimizationvariables and the constraint conditions of the wireless power transfernetwork are set; and the low-complexity algorithm comprises thefollowing steps:

S1. fixing the altitude h, the beam pattern E(θ, ϕ) and the chargingtime τ_(k,γ) of the unmanned aerial vehicle, and solving the objectivefunction with respect to a two-dimensional coordinate (x_(u), y_(u)) ofthe unmanned aerial vehicle by using sequential unconstrained convexminimization (SUCM) at the moment;

S2. fixing the beam pattern E(θ, ϕ) and the charging time τ_(k,γ) basedon the two-dimensional coordinate (x_(u), y_(u)) of the unmanned aerialvehicle, the objective function becoming a monotone decreasing functionwith respect to the altitude h at the moment, and obtaining an optimalaltitude

${h^{*} = {\max\left\{ {\frac{\sqrt{D_{\max}}}{\tan\;\Theta},h_{\min}} \right\}}},$

while D_(max)=max_(k=1, . . . , K) D_(k), and D_(k)=∥z_(k)−z_(u)∥²;

S3. fixing the charging time τ_(k,γ) based on the three-dimensionalposition deployment of the unmanned aerial vehicle, and optimizing theenergy beam pattern by using a multiobjective evolutionary algorithmbased on decomposition (MOEA/D), wherein the energy beam patterncomprises an antenna gain, a minor lobe voltage level and a beam width,and since the antenna gain, the minor lobe voltage level and the beamwidth are functions with respect to a phase the antenna gain, the minorlobe voltage level and the beam width optimized are expressed as amultiobjective optimization problem with respect to the phase_(i)q; andS4. based on the optimal three-dimensional position, the optimalaltitude and the optimal energy beam pattern of the unmanned aerialvehicle which are solved, solving the objective function which is alinear programming problem of a function with respect to the chargingtime r_(k,γ) at the moment by using a standard convex optimization tool.

For further implementation, the step S1 comprises the following steps:

S1.1. initializing iteration times m, a polyhedron S⁽¹⁾={t∈R⁻^(K):−Σ_(k=1) ^(K) t_(k)≤1/

} and a vertex set

${v^{(1)} = {\left\{ {{{- \frac{1}{Ϛ}}e_{k}} \in {{R^{K}\text{:}\mspace{14mu} 1} \leq k \leq K}} \right\}\bigcup\left\{ 0 \right\}}},$

wherein R⁻ ^(K) is a K-dimensional negative real number, and R^(K) is aK-dimensional non-negative real number; a best feasible solution ofmax_(t∈{tilde over (D)})v^(T)t is t*, satisfying q(t₀)<q(t*), wherein t₀is a known quantity, while t* is a solved quantity; q(t)=A_(k)t^(−α/2),and A_(k)=ξ_(k)β₀P₀τ_(k,γ)|E(θ, ϕ)|²;

>0; {tilde over (D)}={t−t₀|t∈D}, D={t∈R₊ ^(K):ε_(k)(x_(u), y_(u))≤t_(k),=1, . . . , K}, and D is a domain of definition of t, {tilde over (D)}is a domain of definition of t−t₀, and ε_(k)(x_(u),y_(u))=(x_(k)−x_(u))²+(y_(k)−y_(u))²+h²;

S1.2. for all −w=v, v∈v^(m), solving min_(x) _(u) _(,y) _(u) Σ_(k=1)^(K) w_(k)[(x_(k)−x_(u))²+(y_(k)−y_(u))²+h²]^(α/2) to obtain optimalvalues μ(w) and (x_(u)*, y_(u)*), wherein

${x_{u}^{*} = \frac{\sum\limits_{k = 1}^{K}{w_{k}x_{k}}}{\sum\limits_{k = 1}^{K}w_{k}}},{{{and}\mspace{14mu} y_{u}^{*}} = \frac{\sum\limits_{k = 1}^{K}{w_{k}y_{k}}}{\sum\limits_{k = 1}^{K}w_{k}}},$

wherein w=[w₁, . . . , w_(k)] is a k-dimensional vector, and v^(m) is am-dimensional vector;

S1.3. judging whether an inequality max_(−w∈v) _(m) −μ(w)+w^(T)t₀≤1 istrue, and if the inequality is true, returning to the S1.1; and if theinequality is not true, skipping to the step S1.4;

S1.4. obtaining {tilde over (w)}=[{tilde over (w)}₁, . . . , {tilde over(w)}_(k)] through max_(−w∈v) _(m) −μ(w)+w^(T)t₀, and {tilde over(t)}_(k)=ε_(k)({tilde over (x)}_(u), {tilde over (y)}_(u)), k=1, . . . ,K, wherein ∈_(k)({tilde over (x)}_(u), {tilde over(y)}_(u))=(x_(k)−{tilde over (x)}_(u))²+(y_(k)−{tilde over(y)}_(u))²+h²; and after obtaining {tilde over (w)} and {tilde over(t)}_(k), further obtaining a two-dimensional position ({tilde over(x)}_(u), {tilde over (y)}_(u)) of the unmanned aerial vehicle, while({tilde over (x)}_(u), {tilde over (y)}_(u)) is obtained respectively bythe following formulas

${{\overset{\sim}{x}}_{u} = \frac{\sum\limits_{k = 1}^{K}{{\overset{\sim}{w}}_{k}x_{k}}}{\sum\limits_{k = 1}^{K}{\overset{\sim}{w}}_{k}}},{{{{and}\mspace{14mu}{\overset{\sim}{y}}_{u}} = \frac{\sum\limits_{k = 1}^{K}{{\overset{\sim}{w}}_{k}y_{k}}}{\sum\limits_{k = 1}^{K}{\overset{\sim}{w}}_{k}}};}$

S1.5. judging whether an inequality q({tilde over (t)})≤q(t*) is true,and if the inequality is true, updating t*={tilde over (t)}, wherein{tilde over (t)}=[{tilde over (t)}₁, . . . , {tilde over (t)}_(k)];otherwise, calculating ϑ and S^((m+1)) by using ϑ=sup{ρ:q(t₀+ρ*({tildeover (t)}−t₀))≤q(t*)} and

$S^{({m + 1})} = {S^{(m)}\bigcap\left\{ {{t^{T}\left( {\overset{\sim}{t} - t_{0}} \right)} \leq \frac{1}{\vartheta}} \right\}}$

S1.6. judging whether iteration times m of the algorithm satisfy settimes, if the set times are not satisfied, m:=m+1, returning to the stepS1.2, and if the set times are satisfied, obtaining the two-dimensionalposition (x_(u)*, y_(u)*) of the unmanned aerial vehicle.

Further, in the step S2, the beam pattern E(θ, ϕ) and the charging timeτ_(k,γ) are fixed based on the obtained two-dimensional position of theunmanned aerial vehicle, and the optimization problem is expressed asfollows at the moment:

$\begin{matrix}{\max\limits_{h}{\sum\limits_{k = 1}^{K}\frac{A_{k}}{\left\lbrack {D_{k} + h^{2}} \right\rbrack^{\alpha/2}}}} & \left( {9a} \right) \\{{{s.t.D_{\max}} \leq {h^{2}\tan\;\Theta}},} & \left( {9b} \right) \\{{h_{\min} \leq h \leq h_{\max}},} & \left( {9c} \right)\end{matrix}$

wherein a constraint condition D_(max)≤12² tan Θ shows that a distancebetween the unmanned aerial vehicle and all the users is not allowed toexceed the coverage radius of the unmanned aerial vehicle; and since theoptimization problem is a convex optimization problem, while theobjective function is a monotone decreasing function with respect to thealtitude h of the unmanned aerial vehicle, then the optimal altitude isas follows:

$\begin{matrix}{h^{*} = {\max\left\{ {\frac{\sqrt{D_{\max}}}{\tan\Theta},h_{\min}} \right\}}} & (10)\end{matrix}$

Further, the step S3 comprises the following steps:

S3.1. fixing the charging time τ_(k,γ) based on the obtainedthree-dimensional position (x_(u)*, y_(u)*, h*) of the unmanned aerialvehicle, so that the objective function is expressed as follows:

$\begin{matrix}{{\max{\sum\limits_{k = 1}^{K}{\eta_{k}{{E\left( {\theta,\phi} \right)}}^{2}}}},{{{wherein}\mspace{14mu}\eta_{k}} = \frac{\xi_{k}\beta_{0}P_{0}\tau_{k,\gamma}}{\left\lbrack {{{z_{k} - z_{u}}}^{2} + h^{2}} \right\rbrack^{\alpha/2}}}} & (11)\end{matrix}$

is a constant; therefore, the objective function is expressed asfollows:

$\begin{matrix}{\max{\sum\limits_{k = 1}^{K}{{E\left( {\theta,\phi} \right)}}^{2}}} & (12)\end{matrix}$

S3.2. modeling into a multiobjective optimization problem, and theobjective functions of the multiobjective optimization problem areexpressed as follows:

min F(β)=(ƒ₁(β),ƒ₂(β),ƒ₃(β))^(T),  (13a)

s.t.β∈R ^(M),  (13b)

wherein ƒ₁(β)=SLL(β): an objective function of a minimized minor lobevoltage level with respect to β;

${{f_{2}(\beta)} = \frac{1}{{E\left( {\theta,\phi} \right)}}}\text{:}$

an objective function of a maximized antenna gain with respect to β; and

${f_{3}(\beta)} = {\frac{1}{\Theta }\text{:}}$

an objective function of a maximized beam width θ of the array antennawith respect to β;

S3.3. definition of domination: assuming that u, v∈R^(m), u dominatingv, and if and only if

u _(i) ≤v _(i) ,∀i∈{1, . . . ,m},  (14)

u _(j) <v _(j) ,∀i∈{1, . . . ,m},  (15)

S3.4. definition of Pareto optimality: x*∈Ω being the Pareto optimality,satisfying a condition that no other solution x∈Ω exists, so that F(x)dominates F(x*), and F(x*) being a Pareto optimal vector; and

S3.5. aiming at the constructed multiobjective optimization problem,using the MOEA/D to generate a directional beam.

Further, the MOEA/D has the specific steps as follows:

A1. inputting: the constructed multiobjective optimization problem;Iter: iteration times; N_(pop)a number of subproblems; K¹, . . . , K^(N)^(pop) : a weight vector; and T_(nei): a number of neighbor vectors ofeach weight vector;

A2. initializing: a set EP=Ø;

A3. for each i=1, . . . , N_(pop), setting ℏ(i)={i₁, . . . , i_(T)_(net) } as an index of the neighbor vector according to T_(nei) weightvectors K¹, . . . , K^(N) ^(pop) near an Euclidean distance weight i themost;

A4. randomly generating an original group β=[β₁, . . . , β_(N) _(pop) ];and setting FV_(i)=F(β_(i));

A5. for each j=1, . . . , d, initializing z=(z₁, . . . , z_(j), . . . ,z_(d))^(T) through z_(j)=min{ƒf_(j)(β), β∈R^(M)}, wherein d is a numberof objective functions;

A6. updating: for each i=1, . . . , N_(pop), randomly selecting twoindexes κ and ι from a set ℏ(i), and combining β_(κ) and β_(ι) togenerate a new feasible solution y by a differential evolutionalgorithm; for each j=1, . . . , d, if z_(j)>ƒ_(j)(y), settingz_(j)=ƒ_(j)(y); at the moment, z_(j) being a current optimal solution;for each j∈ℏ(i), if g^(te)(y|κ^(j), z)≤g^(te)(β_(j)|κ^(j), z), settingβ_(j)=y and FV_(j)=F(y), wherein g^(te)(y|κ^(j),z)=max_(1≤j≤d){κ^(j)|ƒ_(j)(y)−z_(j)}; eliminating a solution dominatedby F(y) from the set EP; and if no vector exists in the set EP todominate F(y), adding F(y) into the set EP;

A7. stopping criterion: if the iteration times satisfy Iter, enteringinto step A8; otherwise, returning to the updating step A6; and

A8. outputting: constantly updating a non-dominant solution EP duringsearching, and finally obtaining an optimal domination set EP*, and aPareto optimal solution β*, so that EP*∈β*.

Further, in the step S4, based on the obtained three-dimensionalposition (x_(u)*, y_(u)*, h*) of the unmanned aerial vehicle and thebeam pattern E*(θ, ϕ), the original problems become

$\begin{matrix}{\max\limits_{\tau_{k,\gamma}}{\sum\limits_{k = 1}^{K}\frac{\xi_{k}\beta_{0}P_{0}\tau_{k,\gamma}{{E\left( {\theta,\phi} \right)}}^{2}}{\left\lbrack {{\left. {z_{k} - z_{u}} \right|}^{2} + h^{2}} \right\rbrack^{\alpha/2}}}} & \left( {16a} \right) \\{{{s.t.{\sum\limits_{\gamma = 1}^{\Gamma}\tau_{k,\gamma}}} = T};} & \left( {16b} \right)\end{matrix}$

The solution of the above problems may lead to serious fairnessproblems, and the reason is that when the total energy harvested in acertain area is significantly greater than that in other areas, thecharging time in this area is longer; and in order to solve thisdifficulty, the following new optimization problems are proposed:

$\begin{matrix}{\max\limits_{\tau_{k,\gamma}}{\sum\limits_{k = 1}^{K}{\min\limits_{k \in K}\frac{\xi_{k}\beta_{0}P_{0}\tau_{k,\gamma}{{E\left( {\theta,\phi} \right)}}^{2}}{\left\lbrack {\left( {x_{k} - x_{u,\gamma}} \right)^{2} + \left( {y_{k} - y_{u,\gamma}} \right)^{2} + h_{\gamma}^{2}} \right\rbrack^{\alpha/2}}}}} & \left( {17a} \right) \\{{{s.t.{\sum\limits_{\gamma = 1}^{\Gamma}\tau_{k,\gamma}}} = T};} & \left( {17b} \right)\end{matrix}$

at the moment, the three-dimensional position of the unmanned aerialvehicle in the area γ is (x_(u,γ), y_(u,γ), h_(γ)); and in order tosolve this problem, an auxiliary variable t is introduced, then:

$\begin{matrix}{\mspace{79mu}{\max\limits_{\tau_{k,\gamma}}t}} & \left( {18a} \right) \\{\mspace{79mu}{{{s.t.{\sum\limits_{\gamma = 1}^{\Gamma}{\tau_{k,\gamma}{\varrho\left( {x_{u,\gamma},\gamma_{u,\gamma},h_{\gamma}} \right)}}}} \geq t},}} & \left( {18b} \right) \\{{{\sum\limits_{\gamma = 1}^{\Gamma}\tau_{k,\gamma}} = T},{{{{wherein}\mspace{14mu}{\varrho\left( {x_{u,\gamma},\gamma_{u,\gamma},h_{\gamma}} \right)}} = {\underset{k = 1}{\sum\limits^{K}}\frac{\xi_{k}\beta_{0}P_{0}\tau_{k,\gamma}{{E\left( {\theta,\phi} \right)}}^{2}}{\left\lbrack {\left( {x_{k} - x_{u,\gamma}} \right)^{2} + \left( {y_{k} - y_{u,\gamma}} \right)^{2} + h_{\gamma}^{2}} \right\rbrack^{\alpha/2}}}};}} & \left( {18c} \right)\end{matrix}$

and the optimization problem is a linear programming problem, which issolved by a general convex optimization tool.

Further, in the step S4:

A1. inputting: the constructed multiobjective optimization problem;Iter: iteration times; N_(pop)a number of subproblems; K¹, . . . , K^(N)^(pop) : a weight vector; and T_(nei): a number of neighbor vectors ofeach weight vector;

A2. initializing: a set EP=Ø;

A3. for each i=1, . . . , N_(pop), setting ℏ(i)={i₁, . . . , i_(T)_(net) } as an index of the neighbor vector according to T_(nei) weightvectors K¹, . . . , K^(N) ^(pop) near an Euclidean distance weight i the

A4. randomly generating an original group β=[β₁, . . . , β_(N) _(pop) ];and setting FV_(i)=F(β_(i));

A5. for each j=1, . . . , d, initializing z=(z₁, . . . , z_(j), . . . ,z_(d))^(T) through z_(j)=min{ƒf_(j)(β), β∈R^(M)}, wherein d is a numberof objective functions;

A6. updating: for each i=1, . . . , N_(pop), randomly selecting twoindexes κ and ι from a set ℏ(i), and combining β_(κ) and β_(ι) togenerate a new feasible solution y by a differential evolutionalgorithm; for each j=1, . . . , d, if z_(j)>ƒ_(j)(y), settingz_(j)=ƒ_(j)(y); at the moment, z_(j) being a current optimal solution;for each j∈ℏ(i), if g^(te)(y|κ^(j), z)≤g^(te)(β_(j)|κ^(j), z), settingβ_(j)=y and FV_(j)=F(y), wherein g^(te)(y|κ^(j),z)=max_(1≤j≤d){κ^(j)|ƒ_(j)(y)−z_(j)}; eliminating a solution dominatedby F(y) from the set EP; and if no vector exists in the set EP todominate F(y), adding F(y) into the set EP;

A7. stopping criterion: if the iteration times satisfy Iter, enteringinto step A8; otherwise, returning to the updating step A6; and

A8. outputting: constantly updating a non-dominant solution EP duringsearching, and finally obtaining an optimal domination set EP*, and aPareto optimal solution β*, so that EP*∈β*.

Further, in the step S4:

based on the obtained three-dimensional position (x_(u)*, y_(u)*, h*) ofthe unmanned aerial vehicle and the beam pattern E*(θ, ϕ), the originalproblems become

$\begin{matrix}{\max\limits_{\tau_{k,\gamma}}{\sum\limits_{k = 1}^{K}\frac{\xi_{k}\beta_{0}P_{0}\tau_{k,\gamma}{{E\left( {\theta,\phi} \right)}}^{2}}{\left\lbrack {{{z_{k} - z_{u}}}^{2} + h^{2}} \right\rbrack^{\alpha/2}}}} & \left( {16a} \right) \\{{{s.t.{\sum\limits_{\gamma = 1}^{\Gamma}\tau_{k,\gamma}}} = T};} & \left( {16b} \right)\end{matrix}$

based on the obtained three-dimensional position (x_(u)*, y_(u)*, h*) ofthe unmanned aerial vehicle and the beam pattern E*(θ, ϕ), originalproblem become

$\begin{matrix}{\max\limits_{\tau_{k,\gamma}}{\sum\limits_{k = 1}^{K}\frac{\xi_{k}\beta_{0}P_{0}\tau_{k,\gamma}{{E\left( {\theta,\phi} \right)}}^{2}}{\left\lbrack {{{z_{k} - z_{u}}}^{2} + h^{2}} \right\rbrack^{\alpha/2}}}} & \left( {16a} \right) \\{{{s.t.{\sum\limits_{\gamma = 1}^{\Gamma}\tau_{k,\gamma}}} = T};} & \left( {16b} \right)\end{matrix}$

The solution of the above problems may lead to serious fairnessproblems, and the reason is that when the total energy harvested in acertain area is significantly greater than that in other areas, thecharging time in this area is longer; and in order to solve thisdifficulty, the following new optimization problems are proposed:

$\begin{matrix}{\max\limits_{\tau_{k,\gamma}}{\sum\limits_{k = 1}^{K}{\min\limits_{k \in K}\frac{\xi_{k}\beta_{0}P_{0}\tau_{k,\gamma}{{E\left( {\theta,\phi} \right)}}^{2}}{\left\lbrack {\left( {x_{k} - x_{u,\gamma}} \right)^{2} + \left( {y_{k} - y_{u,\gamma}} \right)^{2} + h_{\gamma}^{2}} \right\rbrack^{\alpha/2}}}}} & \left( {17a} \right) \\{{{s.t.{\sum\limits_{\gamma = 1}^{\Gamma}\tau_{k,\gamma}}} = T};} & \left( {17b} \right)\end{matrix}$

at the moment, the three-dimensional position of the unmanned aerialvehicle in the area y is (x_(u,γ), y_(u,γ), h_(γ)); and in order tosolve this problem, an auxiliary variable t is introduced, then:

$\begin{matrix}{\mspace{79mu}{\max\limits_{\tau_{k,\gamma}}t}} & \left( {18a} \right) \\{\mspace{79mu}{{{s.t.{\sum\limits_{\gamma = 1}^{\Gamma}{\tau_{k,\gamma}{\varrho\left( {x_{u,\gamma},\gamma_{u,\gamma},h_{\gamma}} \right)}}}} \geq t},}} & \left( {18b} \right) \\{\mspace{79mu}{{{{{{\sum\limits_{\gamma = 1}^{\Gamma}\tau_{k,\gamma}} = T},\mspace{79mu}{wherein}}{\varrho\left( {x_{u,\gamma},y_{u,\gamma},\ h_{\gamma}} \right)}} = {\sum_{k = 1}^{K}\frac{\xi_{k}\beta_{0}P_{0}\tau_{k,\gamma}{{E\left( {\theta,\phi} \right)}}^{2}}{\left\lbrack {\left( {x_{k} - x_{u,\gamma}} \right)^{2} + \left( {y_{k} - y_{u,\gamma}} \right)^{2} + h_{\gamma}^{2}} \right\rbrack^{\alpha/2}}}};}} & \left( {18c} \right)\end{matrix}$

and the optimization problem is a linear programming problem, which issolved by a general convex optimization tool.

In step 4, a three-dimensional flight trajectory of the unmanned aerialvehicle is designed based on Branch and Bound.

An objective function of optimization problems based on a minimizedflight distance is the minimized flight distance, which is expressed asfollows:

$\begin{matrix}{{\underset{a \neq b}{\sum\limits_{a = 0}^{\Gamma}}{\underset{a \neq b}{\sum\limits_{b = 0}^{\Gamma}}{d_{ab}x_{ab}}}},} & (19)\end{matrix}$

optimization variables of the optimization problems are able to beexpressed as:

1> a distance d_(ab)=√{square root over((x_(a)−x_(b))²+(y_(a)−y_(b))²+(h_(a)−h_(b))²)} between a hoveringposition a with a coordinate (x_(a), y_(a), h_(a)) and a hoveringposition b with a coordinate (x_(b), y_(b), h_(b)); and

2> a non-negative integer x_(ab)∈{0,1};

constraint conditions of the optimization problem comprise:

1] a number of times of flying from the hovering position a to thehovering position b being no more than 1:

${{\sum_{\underset{a \neq b}{a = 0}\ }^{\Gamma}x_{ab}} = 1};$

2] a number of times of flying from the hovering position b to thehovering position a being no more than 1:

${{\sum\limits_{\underset{b \neq a}{b = 0}}^{\Gamma}\; x_{ab}} = 1};$

3] a number of times of flying from the hovering position a to anoriginal position 0 is no more than 1: Σ_(a=1) ^(Γ) x_(a0)=1; and

4] a number of times of staying on the hovering position being no morethan γ: μ_(a)−μ_(b)+γx_(ab)≤γ−1, wherein γ>Γ, μ_(a) and μ_(b) arearbitrary real variables, and a=1, . . . , Γ, b=1, . . . , Γ;

the optimization problems based on the minimized flight distance are asfollows:

$\begin{matrix}{\min{\underset{a \neq b}{\sum\limits_{a = 0}^{\Gamma}}{\underset{b \neq a}{\sum\limits_{b = 0}^{\Gamma}}{d_{ab}x_{ab}}}}} & \left( {20a} \right) \\{{{s.t.{\underset{a \neq b}{\sum\limits_{a = 0}^{\Gamma}}x_{ab}}} = 1},} & \left( {20b} \right) \\{{{\underset{b \neq a}{\sum\limits_{b = 0}^{\Gamma}}x_{ab}} = 1},} & \left( {20c} \right) \\{{{\sum\limits_{a = 1}^{\Gamma}x_{a0}} = 1},} & \left( {20d} \right) \\{{{\mu_{a} - \mu_{b} + {\gamma x_{ab}}} \leq {\gamma - 1}};} & \left( {20e} \right)\end{matrix}$

the steps for obtaining the optimal flight trajectory by Branch andBound are as follows:

firstly, decomposing all flight trajectory sets, namely feasiblesolutions, into smaller sets by the low-complexity algorithm, andcalculating a lower bound of each set; then, containing a set of asmallest lower bound in all the sets in the optimal trajectory; andfinally, forming all the selected sets into the optimal flighttrajectory.

The invention proposes to apply a three-dimensional energy beam formingtechnology to the wireless power transfer network, establishes amathematical optimization problem of the network model based onmaximizing the energy harvested by the user, and applies thelow-complexity iterative algorithms to jointly optimize thethree-dimensional position deployment of the unmanned aerial vehicle,the charging time and the energy beam pattern to maximize the energyharvested by the user in a coverage area while meeting restrictions onan altitude and the coverage area of the unmanned aerial vehicle.

The foregoing is only the preferred embodiments of the presentinvention, but the scope of protection of the present invention is notlimited to this. The equivalent substitutions or changes made by thoseskilled in the art according to the technical solutions and theinventive concept of the present invention within the scope disclosed bythe present invention all belong to the scope of protection of thepresent invention.

1. A method for designing a three-dimensional trajectory of an unmanned aerial vehicle based on a wireless power transfer network, comprising the following steps of: step 1: establishing a downlink channel model of the wireless power transfer network: combining a three-dimensional dynamic energy beam forming with a direct path to form a channel model between an unmanned aerial vehicle and a user; step 2: establishing a mathematical model based on maximizing energy harvested by a user, comprising mathematical expressions for determining an optimization variable, an objective function and a constraint condition; step 3: establishing a low-complexity iterative algorithm for jointly optimizing a three-dimensional position deployment of the unmanned aerial vehicle, a charging time and an energy beam; and step 4: designing a three-dimensional flight trajectory of the unmanned aerial vehicle based on branch and bound method, wherein, in the step 1: the wireless power transfer network comprises a quadrotor unmanned aerial vehicle and K users randomly distributed on land, the unmanned aerial vehicle is provided with a linear array comprising M antenna elements, while the users on land are provided with a single antenna; a land geometric area is divided into Γ service areas; a position coordinate of a user k is z_(k)=(x_(k), y_(k), 0), and k∈{1, . . . , K} is an index of an user set; a three-dimensional position of the unmanned aerial vehicle is z_(u)=(x_(u), y_(u), h), and h represents an altitude of the umnanned aerial vehicle; and a wireless channel between the umnanned aerial vehicle and the user k is dominated by the direct path, so that a channel vector h_(k) is as follows: h _(k)=√{square root over (β₀ d _(k) ^(α))}α(θ,ϕ), wherein n_(k)=β₀d_(k) ⁻¹ is a multiplexing coefficient, and β₀ is a channel power gain when a reference distance is 1 m; in addition, d_(k)=√{square root over ((x_(k)−x_(u))²+(y_(k)−y_(u))₂+h²)} is a distance between the unmanned aerial vehicle and the user k, α is a path loss coefficient; and a(θ, ϕ) is a direction vector, which is expressed as follows: a(θ,ϕ)=[1,e ^(j2π/λd) ^(array) ^(sin θ cos ϕ) , . . . ,e ^(j(M-1)2π/λd) ^(array) ^(sin θ cos ϕ)]^(T), wherein λ and d_(array) are respectively a wavelength and an element spacing in the linear array, and an elevation angle θ and an azimuth angle ϕ are known quantities; therefore, a channel gain between the unmanned aerial vehicle and the user k is expressed as follows: ${{h_{k}^{H}w}}^{2} = {\frac{\beta_{0}}{\left\lbrack {\left( {x_{k} - x_{u}} \right)^{2} + \left( {y_{k} - y_{u}} \right)^{2} + h^{2}} \right\rbrack^{\alpha/2}}{{{a^{H}\left( {\theta,{\phi\; w}} \right.}^{2},}}}$ wherein H represents conjugate transpose, w is a beam weight vector, and a main lobe direction is controlled by adjusting a weight value; and E(θ, ϕ)=a^(H)(θ, ϕ)w is a synthesized pattern of the linear array; the linear array installed on the unmanned aerial vehicle as a transmitting end is divided into t sub-arrays, and each sub-array independently generates an energy beam to aim at a certain user; therefore, for the linear array comprising M antenna elements, an array factor and a synthesized pattern are expressed as follows: ${{AF} = {\sum\limits_{m = 1}^{M = 1}{I_{m} \times e^{{j{({m - 1})}}{({{\kappa\beta sin\theta cos\phi} + \beta})}}}}},{{E\left( {\theta,\phi} \right)} = {\sum\limits_{m = 1}^{M = 1}{{p_{m}\left( {\theta,\phi} \right)}I_{m} \times e^{{j{({m - 1})}}{({{\kappa\; d\;\sin\;{\theta cos\phi}} + \beta})}}}}},$ wherein κ=2π/λ, p_(m)(θ, ϕ) and I_(m) are respectively an element pattern and an excitation amplitude of an m^(th) antenna element, and β is a uniformly graded phase; and d is an array element spacing, and e is a natural constant.
 2. (canceled)
 3. The method for designing the three-dimensional trajectory of the unmanned aerial vehicle based on the wireless power transfer network according to claim 1, wherein, in the step 2: total energy harvested by the user k is expressed as follows: $\begin{matrix} {Q_{k} = {\xi_{k}{{h_{k}^{H},w}}^{2}P_{0}\tau_{k,\gamma}}} & \left\lbrack \lbrack 6\rbrack \right\rbrack \\ {{= \frac{\xi_{k}\beta_{0}P_{0}\tau_{k,\gamma}{{E\left( {\theta,\phi} \right)}}^{2}}{\left\lbrack {\left( {x_{k} - x_{u}} \right)^{2} + \left( {y_{k} - y_{u}} \right)^{2} + h^{2}} \right\rbrack^{\alpha/2}}},} & \left\lbrack \lbrack 7\rbrack \right\rbrack \end{matrix}$ wherein ξ_(k) is an energy conversion efficiency, 0<ξ_(k)<1, P₀ is a transmitting power of the unmanned aerial vehicle, and τ_(k,γ) is a charging time of the user k in a γ^(th) area; optimization variables of the mathematical model based on maximizing the energy harvested by the user comprise: a two-dimensional coordinate of the unmanned aerial vehicle, which is namely z_(u)=(x_(u), y_(u), 0); an altitude h of the unmanned aerial vehicle; an energy beam pattern E(θ, ϕ) of the linear array; and a charging time τ_(k,γ) of the user k located in the γ^(th) service area; constraint conditions of the mathematical model based on maximizing the energy harvested by the user comprise: a maximum horizontal distance between the unmanned aerial vehicle and the user being no more than a coverage radius of the unmanned aerial vehicle: ∥z_(k)−z_(u)∥²≤h² tan² θ; and θ being a beam width; a total charging time of the unmanned aerial vehicle in all the r service areas being no more than a charging period T: Σ_(γ=1) ^(Γ) τ_(k,γ)=T; the altitude of the unmanned aerial vehicle being constrained to: h_(min)<h<h_(max), wherein h_(min) and h_(max) are respectively a lowest altitude and a highest altitude that the unmanned aerial vehicle is able to reach; the mathematical model based on maximizing the energy harvested by the user is as follows: $\begin{matrix} {\max\limits_{{\mathfrak{Z}}_{u},h,\tau_{k,\gamma},{E{({\theta,\phi})}}}{\sum\limits_{k = 1}^{K}\frac{\xi_{k}\beta_{0}P_{0}\tau_{k,\gamma}{{E\left( {\theta,\phi} \right.}^{2}}}{\left\lbrack {{{z_{k} - z_{u}}}^{2} + h^{2}} \right\rbrack^{\alpha/2}}}} & \left\lbrack \left\lbrack \left( {8a} \right) \right\rbrack \right\rbrack \\ {{{s.t.\mspace{11mu}{{z_{k} - z_{u}}}^{2}} \leq {h^{2}\mspace{11mu}\tan^{2}\Theta}},} & \left\lbrack \left\lbrack \left( {8b} \right) \right\rbrack \right\rbrack \\ {{{\overset{\Gamma}{\sum\limits_{\gamma = 1}}\tau_{k,\gamma}} = T}\ ,} & \left\lbrack \left\lbrack \left( {8c} \right) \right\rbrack \right\rbrack \\ {h_{\min} < h < {h_{mc\iota x}.}} & \left\lbrack \left\lbrack \left( {8d} \right) \right\rbrack \right\rbrack \end{matrix}$
 4. The method for designing the three-dimensional trajectory of the unmanned aerial vehicle based on the wireless power transfer network according to claim 1, wherein, in the step 3, system parameters, a value range of the optimization variables and the constraint conditions of the wireless power transfer network are set; and the low-complexity iterative algorithm comprises the following steps: S1. fixing the altitude h, the beam pattern E(θ, ϕ) and the charging time τ_(k,γ) of the unmanned aerial vehicle, and solving the objective function with respect to a two-dimensional coordinate (x_(u), y_(u)) of the unmanned aerial vehicle by using sequential unconstrained convex minimization at the moment; S2. fixing the beam pattern E(θ, ϕ) and the charging time τ_(k,γ) based on the two-dimensional coordinate (x_(u), y_(u)) of the unmanned aerial vehicle, the objective function becoming a monotone decreasing function with respect to the altitude h at the moment, and obtaining an optimal altitude ${h^{*} = {\max\left\{ {\frac{\sqrt{D_{\max}}}{\tan\;\Theta},h_{\min}} \right\}}},$  while D_(max)=max_(k=1, . . . , K) D_(k), and D_(k)=∥z_(k)−z_(u)∥²; S3. fixing the charging tune τ_(k,γ) based on the three-dimensional position deployment of the unmanned aerial vehicle, and optimizing the energy beam pattern by using a multiobjective evolutionary algorithm based on decomposition, wherein the energy beam pattern comprises an antenna gain, a minor lobe voltage level and a beam width, and since the antenna gain, the minor lobe voltage level and the beam width are functions with respect to a phase β, the antenna gain, the minor lobe voltage level and the beam width optimized are expressed as a multiobjective optimization problem with respect to the phase β; and S4. based on the optimal three-dimensional position, the optimal altitude and the optimal energy beam pattern of the unmanned aerial vehicle which are solved, solving the objective function which is a linear programming problem of a function with respect to the charging time τ_(k,γ) at the moment by using a standard convex optimization tool.
 5. The method for designing the three-dimensional trajectory of the unmanned aerial vehicle based on the wireless power transfer network according to claim 4, wherein, the step S1 comprises the following steps: S1.1. initializing iteration times m, a polyhedron $S^{(1)} = \left\{ {t \in {{{R_{-}^{K}\text{:}} - {\sum_{k = 1}^{K}t_{k}}} \leq \frac{1}{\varsigma}}} \right\}$ and a vertex set ${v^{(1)} = {\left\{ {{{- \frac{1}{ϛ}}e_{k}} \in {{R^{K}\text{:}1} \leq k \leq K}} \right\}\bigcup\left\{ 0 \right\}}},$ wherein R⁻ ^(K) is a K-dimensional negative real number, and R^(K) is a K-dimensional non-negative real number; a best feasible solution of max_(t∈{tilde over (D)})v^(T)t is t*, satisfying q(t₀)<q(t*), wherein t₀ is a known quantity, while t* is a solved quantity; q(t)=A_(k)t^(−α/2), and A_(k)=ξ_(k)β₀P₀τ_(k,γ)|E(θ, ϕ)|²;

>0; {tilde over (D)}={t−t₀|t∈D}, D={t∈R₊ ^(K):ε_(k)(x_(u), y_(u))≤t_(k), =1, . . . , K}, and D is a domain of definition of t, {tilde over (D)} is a domain of definition of t−t₀, and ε_(k)(x_(u), y_(u))=(x_(k)−x_(u))²+(y_(k)−y_(u))²+h²; S1.2. for all −w=v, v∈v^(m), solving min_(x) _(u) _(,y) _(u) Σ_(k=1) ^(K) w_(k)[(x_(k)−x_(u))²+(y_(k)−y_(u))²+h²]^(α/2) to obtain optimal values μ(w) and (x_(u)*, y_(u)*), wherein ${x_{u}^{*} = \frac{\sum_{k = 1}^{K}{w_{k}x_{k}}}{\sum_{k = 1^{w_{k}}}^{K}}},{and}$ ${y_{u}^{*} = \frac{\sum_{k = 1}^{K}{w_{k}y_{k}}}{\sum_{k = 1^{w_{k}}}^{K}}},$ wherein w=[w₁, . . . , w_(k)] is a k-dimensional vector, and v^(m) is a m-dimensional vector; S1.3. judging whether an inequality max_(−w∈v) _(m) −μ(w)+w^(T)t₀≤1 is true, and if the inequality is true, returning to the S1.1; and if the inequality is not true, skipping to the step S1.4; S1.4. obtaining {tilde over (w)}=[{tilde over (w)}₁, . . . , {tilde over (w)}_(k)] through max_(−w∈v) _(m) −μ(w)+w^(T)t₀, and {tilde over (t)}_(k)=ε_(k)({tilde over (x)}_(u), {tilde over (y)}_(u)), k=1, . . . , K, wherein ∈_(k)({tilde over (x)}_(u), {tilde over (y)}_(u))=(x_(k)−{tilde over (x)}_(u))²+(y_(k)−{tilde over (y)}_(u))²+h²; and after obtaining {tilde over (w)} and {tilde over (t)}_(k), further obtaining a two-dimensional position ({tilde over (x)}_(u), {tilde over (y)}_(u)) of the unmanned aerial vehicle, while ({tilde over (x)}_(u), {tilde over (y)}_(u)) is obtained respectively by the following formulas ${{\overset{\sim}{x}}_{u} = {{\frac{\sum_{k = 1}^{K}{{\overset{\sim}{w}}_{k}x_{k}}}{\sum_{k = 1}^{K}{\overset{\sim}{w}}_{k}}\mspace{14mu}{and}\mspace{14mu}{\overset{\sim}{y}}_{u}} = \frac{\sum_{k = 1}^{K}{{\overset{\sim}{w}}_{k}y_{k}}}{\sum_{k = 1}^{K}{\overset{\sim}{w}}_{k}}}};$ S1.5. judging whether an inequality q({tilde over (t)})≤q(t*) is true, and if the inequality is true, updating t*={tilde over (t)}, wherein {tilde over (t)}=[{tilde over (t)}₁, . . . , {tilde over (t)}_(k)]; otherwise, calculating ϑ and S^((m+1)) by using $\vartheta = {{\sup\left\{ {\rho:{{q\left( {t_{0} + {\rho*\left( {\overset{\sim}{t} - t_{0}} \right)}} \right)} \leq {q\left( t^{*} \right)}}} \right\}\mspace{14mu}{and}\mspace{14mu} S^{({m + 1})}}\bigcap\left\{ {{t^{T}\left( {\overset{\sim}{t} - t_{0}} \right)} \leq \frac{1}{\vartheta}} \right\}}$  respectively, wherein ε≥1; and under a condition of obtaining variables ρ and ϑ, using an analytic center cutting-plane method (ACCPM) algorithm to cut the polyhedron; and S1.6. judging whether iteration times m of the algorithm satisfy set times, if the set times are not satisfied, m:=m+1, returning to the step S1.2, and if the set times are satisfied, obtaining the two-dimensional position (x_(u)*, y_(u)*) of the unmanned aerial vehicle.
 6. The method for designing the three-dimensional trajectory of the unmanned aerial vehicle based on the wireless power transfer network according to claim 4, wherein, in the step S2, the beam pattern E(θ, ϕ) and the charging time τ_(k,γ) are fixed based on the obtained two-dimensional position of the unmanned aerial vehicle, and the optimization problem is expressed as follows at the moment: $\begin{matrix} {\max\limits_{h}{\sum\limits_{k = 1}^{K}\frac{A_{k}}{\left\lbrack {D_{k} + h^{2}} \right\rbrack^{\alpha/2}}}} & \left\lbrack \left\lbrack \left( {9a} \right) \right\rbrack \right\rbrack \\ {{{s.t.\mspace{14mu} D_{\max}} \leq {h^{2}\tan\;\Theta}},} & \left\lbrack \left\lbrack \left( {9b} \right) \right\rbrack \right\rbrack \\ {{h_{\min} \leq h \leq h_{\min}},} & \left\lbrack \left\lbrack \left( {9c} \right) \right\rbrack \right\rbrack \end{matrix}$ wherein a constraint condition D_(max)≤h² tan θ shows that a distance between the unmanned aerial vehicle and all the users is not allowed to exceed the coverage radius of the unmanned aerial vehicle; and since the optimization problem is a convex optimization problem, while the objective function is a monotone decreasing function with respect to the altitude h of the unmanned aerial vehicle, then the optimal altitude is as follows: $\begin{matrix} {h^{*} = {\max{\left\{ {\frac{\sqrt{D}}{\tan\Theta},h_{\min}} \right\}.}}} & \left\lbrack \left\lbrack (10) \right\rbrack \right\rbrack \end{matrix}$
 7. The method for designing the three-dimensional trajectory of the unmanned aerial vehicle based on the wireless power transfer network according to claim 4, wherein, the step S3 comprises the following steps: S3.1. fixing the charging time τ_(k,γ) based on the obtained three-dimensional position (x_(u)*, y_(u)*, h*) of the unmanned aerial vehicle, so that the objective function is expressed as follows: $\begin{matrix} {{\max{\sum\limits_{k = 1}^{K}{\eta_{k}{{E\left( {\theta,\phi} \right)}}^{2}}}},{{{wherein}\mspace{14mu}\eta_{k}} = \frac{\xi_{k}\beta_{0}p_{0}\tau_{k,\gamma}}{\left\lbrack {{{z_{k} - z_{u}}}^{2} + h^{2}} \right\rbrack^{\alpha/2}}}} & \left\lbrack \left\lbrack \left( {11} \right) \right\rbrack \right\rbrack \end{matrix}$  is a constant; therefore, the objective function is expressed as follows: $\begin{matrix} {{\max{\sum\limits_{k = 1}^{K}{{E\left( {\theta,\phi} \right)}}^{2}}};} & \left\lbrack \left\lbrack \left( {12} \right) \right\rbrack \right\rbrack \end{matrix}$ S3.2. modeling into a multiobjective optimization problem, and the objective functions of the multiobjective optimization problem are expressed as follows: min F(β)=(ƒ₁(β),ƒ₂(β),ƒ₃(β))^(T), s.t.β∈R ^(M), wherein ƒ₁(β)=SLL(β): an objective function of a minimized minor lobe voltage level with respect to β; ${{f_{2}(\beta)} = \frac{1}{{E\left( {\theta,\phi} \right)}}}:$  an objective function of a maximized antenna gain with respect to β; and ${f_{a}(\beta)} = {\frac{1}{\Theta }:}$ an objective function of a maximized beam width θ of the array antenna with respect to β; S3.3. definition of domination: assuming that u, v∈R^(m), u dominating v, and if and only if u _(i) ≤v _(i) ,∀i∈{1, . . . ,m}, u _(j) <v _(j) ,∀i∈{1, . . . ,m}, S3.4. definition of Pareto optimality: x*∈Ω being the Pareto optimality, satisfying a condition that no other solution x∈Ω exists, so that F(x) dominates F(x*), and F(x*) being a Pareto optimal vector; and S3.5. aiming at the constructed multiobjective optimization problem, using the multiobjective evolutionary algorithm based on decomposition to generate a directional beam.
 8. The method for designing the three-dimensional trajectory of the unmanned aerial vehicle based on the wireless power transfer network according to claim 7, wherein the multiobjective evolutionary algorithm based on decomposition comprises the specific steps as follows: A1. inputting: the constructed multiobjective optimization problem; Iter: iteration times; N_(pop)a number of subproblems; K¹, . . . , K^(N) ^(pop) : a weight vector; and T_(nei): a number of neighbor vectors of each weight vector; A2. initializing: a set EP=Ø; A3. for each i=1, . . . , N_(pop), setting ℏ(i)={i₁, . . . , i_(T) _(net) } as an index of the neighbor vector according to T_(nei) weight vectors K¹, . . . , K^(N) ^(pop) near an Euclidean distance weight i the most; A4. randomly generating an original group β=[β₁, . . . , β_(N) _(pop) ]; and setting FV_(i)=F(β_(i)); A5. for each j=1, . . . , d, initializing z=(z₁, . . . , z_(j), . . . , z_(d))^(T) through z_(j)=min{ƒf_(j)(β), β∈R^(M)}, wherein d is a number of objective functions; A6. updating: for each i=1, . . . , N_(pop), randomly selecting two indexes κ and ι from a set ℏ(i), and combining β_(κ) and β_(ι) to generate a new feasible solution y by a differential evolution algorithm; for each j=1, . . . , d, if z_(j)>ƒ_(j)(y), setting z_(j)=ƒ_(j)(y); at the moment, z_(j) being a current optimal solution; for each j∈ℏ(i), if g^(te)(y|κ^(j), z)≤g^(te)(β_(j)|κ^(j), z), setting β_(j)=y and FV_(j)=F(y), wherein g^(te)(y|κ^(j), z)=max_(1≤j≤d){κ^(j)|ƒ_(j)(y)−z_(j)}; eliminating a solution dominated by F(y) from the set EP; and if no vector exists in the set EP to dominate F(y), adding F(y) into the set EP; A7. stopping criterion: if the iteration times satisfy Iter, entering into step A8; otherwise, returning to the updating step A6; and A8. outputting: constantly updating a non-dominant solution EP during searching, and finally obtaining an optimal domination set EP*, and a Pareto optimal solution β*, so that EP*∈β*.
 9. The method for designing the three-dimensional trajectory of the unmanned aerial vehicle based on the wireless power transfer network according to claim 4, wherein in the step S4: based on the obtained three-dimensional position (x_(u)*, y_(u)*, h*) of the unmanned aerial vehicle and the beam pattern E*(θ, ϕ), the original problems become: $\begin{matrix} {\max\limits_{\tau_{k,\gamma}}{\sum\limits_{k = 1}^{K}\frac{\xi_{k}\beta_{0}p_{0}\tau_{k,\gamma}{{E\left( {\theta,\phi} \right)}}^{2}}{\left\lbrack {{{z_{k} - z_{u}}}^{2} + h^{2}} \right\rbrack^{\alpha/2}}}} & \left\lbrack \left\lbrack \left( {16a} \right) \right\rbrack \right\rbrack \\ {{{s.t.{\sum\limits_{\gamma = 1}^{\Gamma}\tau_{k,\gamma}}} = T};} & \left\lbrack \left\lbrack \left( {16b} \right) \right\rbrack \right\rbrack \end{matrix}$ the following new optimization problems are proposed: $\begin{matrix} {\max\limits_{\tau_{k,\gamma}}{\sum\limits_{k = 1}^{K}{\min\limits_{k \in K}\frac{\xi_{k}\beta_{0}p_{0}\tau_{k,\gamma}{{E\left( {\theta,\phi} \right)}}^{2}}{\left\lbrack {\left( {x_{k} - x_{u,\gamma}} \right)^{2} + \left( {y_{k} - y_{u,\gamma}} \right)^{2} + h_{\gamma}^{2}} \right\rbrack^{\alpha/2}}}}} & \left\lbrack \left\lbrack \left( {17a} \right) \right\rbrack \right\rbrack \\ {{{s.t.{\sum\limits_{\gamma = 1}^{\Gamma}\tau_{k,\gamma}}} = T};} & \left\lbrack \left\lbrack \left( {17b} \right) \right\rbrack \right\rbrack \end{matrix}$ at the moment, the three-dimensional position of the unmanned aerial vehicle in the area y is (x_(u,γ), y_(u,γ), h_(γ)); and an auxiliary variable t is introduced, then: $\begin{matrix} {\mspace{79mu}{\max\limits_{\tau_{k,\gamma}}t}} & \left\lbrack \left\lbrack \left( {18a} \right) \right\rbrack \right\rbrack \\ {\mspace{79mu}{{{s.t.{\sum\limits_{\gamma = 1}^{\Gamma}{\tau_{k,\gamma}{\varrho\left( {x_{u,\gamma},y_{u,\gamma},h_{\gamma}} \right)}}}} \geq t},}} & \left\lbrack \left\lbrack \left( {18b} \right) \right\rbrack \right\rbrack \\ {{{\sum\limits_{\gamma = 1}^{\Gamma}\tau_{k,\gamma}} = T},{{{{wherein}\mspace{14mu}{\varrho\left( {x_{u,\gamma},y_{u,\gamma},h_{\gamma}} \right)}} = {\sum_{k = 1}^{K}\frac{\xi_{k}\beta_{0}p_{0}\tau_{k,\gamma}{{E\left( {\theta,\phi} \right)}}^{2}}{\left\lbrack {\left( {x_{k} - x_{u,\gamma}} \right)^{2} + \left( {y_{k} - y_{u,\gamma}} \right)^{2} + h_{\gamma}^{2}} \right\rbrack^{\alpha/2}}}};}} & \left\lbrack \left\lbrack \left( {18c} \right) \right\rbrack \right\rbrack \end{matrix}$  and the optimization problem is a linear programming problem, which is solved by a convex optimization tool.
 10. The method for designing the three-dimensional trajectory of the unmanned aerial vehicle based on the wireless power transfer network according to claim 1, wherein in the step 4: an objective function of optimization problems based on a minimized flight distance is the minimized flight distance, which is expressed as follows: $\begin{matrix} {{\sum\limits_{{a = 0}{a \neq b}}^{\Gamma}{\sum\limits_{{b = 0}{a \neq b}}^{\Gamma}{d_{ab}x_{ab}}}},} & \left\lbrack \left\lbrack (19) \right\rbrack \right\rbrack \end{matrix}$ optimization variables of the optimization problems are able to be expressed as: a distance d_(ab)=√{square root over ((x_(a)−x_(b))²+(y_(a)−y_(b))²+(h_(a)−h_(b))²)} between a hovering position a with a coordinate (x_(a), y_(a), h_(a)) and a hovering position b with a coordinate (x_(b), y_(b), h_(b)); and a non-negative integer x_(ab)∈{0,1}; constraint conditions of the optimization problem comprise: a number of times of flying from the hovering position a to the hovering position b being no more than 1: ${{\sum_{{\alpha = 0}{a \neq b}}^{\Gamma}x_{ab}} = 1};$ a number of times of flying from the hovering position b to the hovering position a being no more than 1: ${{\sum_{{\alpha = 0}{b \neq a}}^{\Gamma}x_{ab}} = 1};$ a number of times of flying from the hovering position a to an original position a is no more than 1: Σ_(a=1) ^(Γ) x_(a0)=1; and 4] a number of times of staying on the hovering position being no more than γ: μ_(a)−μ_(b)+γx_(ab)≤γ−1, wherein γ>Γ, μ_(a) and μ_(b) are arbitrary real variables, and a=1, . . . , Γ, b=1, . . . , Γ; the optimization problems based on the minimized flight distance are as follows: $\begin{matrix} {\min{\sum\limits_{{a = 0}{a \neq b}}^{\Gamma}{\sum\limits_{{b = 0}{b \neq a}}^{\Gamma}{d_{ab}x_{ab}}}}} & \left\lbrack \left\lbrack \left( {20a} \right) \right\rbrack \right\rbrack \\ {{{s.t.{\sum\limits_{{a = 0}{a \neq b}}^{\Gamma}x_{ab}}} = 1},} & \left\lbrack \left\lbrack \left( {20b} \right) \right\rbrack \right\rbrack \\ {{{\sum\limits_{{b = 0}{b \neq a}}^{\Gamma}x_{ab}} = 1},} & \left\lbrack \left\lbrack \left( {20c} \right) \right\rbrack \right\rbrack \\ {{{\sum\limits_{\alpha = 1}^{\Gamma}x_{a\; 0}} = 1},} & \left\lbrack \left\lbrack \left( {20d} \right) \right\rbrack \right\rbrack \\ {{{\mu_{a} - \mu_{b} + {\gamma x_{ab}}} \leq {\gamma - 1}};} & \left\lbrack \left\lbrack \left( {20e} \right) \right\rbrack \right\rbrack \end{matrix}$ the steps for obtaining the optimal flight trajectory by branch and bound method are as follows: firstly, decomposing all flight trajectory sets, namely feasible solutions, into smaller sets by the low-complexity algorithm, and calculating a lower bound of each set; then, containing a set of a smallest lower bound in all the sets in the optimal trajectory; and finally, forming all the selected sets into the optimal flight trajectory. 